Validity as a primitive

Analysis 72 (3):421-430 (2012)
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Abstract

A number of recent works consider treating validity as a primitive notion rather than one defined in some standard manner. There seem to have been three motivations. First, to understand how truth and validity interact in potentially paradoxical settings. Second, to argue that validity is in fact afflicted with paradoxes analogous to the semantic paradoxes. Third, to develop a ‘deflationary’ conception of validity or consequence. This article treats the notion of validity as a primitive notion and shows how to provide a consistent theory of classical validity (and self-applicative truth), conservative over Peano arithmetic

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Citations of this work

Faithfulness for naive validity.Ulf Hlobil - 2019 - Synthese 196 (11):4759-4774.
The Cut‐Free Approach and the Admissibility‐Curry.Ulf Hlobil - 2018 - Thought: A Journal of Philosophy 7 (1):40-48.
There is No Paradox of Logical Validity.Roy T. Cook - 2014 - Logica Universalis 8 (3-4):447-467.

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References found in this work

Saving truth from paradox.Hartry H. Field - 2008 - New York: Oxford University Press.
What are logical notions?Alfred Tarski - 1986 - History and Philosophy of Logic 7 (2):143-154.
Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
An Axiomatic Approach to Self-Referential Truth.Harvey Friedman & Michael Sheard - 1987 - Annals of Pure and Applied Logic 33 (1):1--21.
Logicality and Invariance.Denis Bonnay - 2006 - Bulletin of Symbolic Logic 14 (1):29-68.

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